Is this of any help to the problem described?
No, zero stiffness is not the problem, with J!=0 Nastran still delivers a result.
I simplified the modell again, no more RBE3, just four plate elements and the rod.
Why does it solve?
PARAM,AUTOSPC,NO
PARAM,MAXRATIO,1.E+8
PARAM,GRDPNT,0
CORD2C...